Assuming the OP is meeting for a physical lesson, given that he doesn't want to have the lesson at home due to the teacher talking in heathen lingo and distracting his housemates whereas if it was an online thing a simple pair of headphones would address that ....
I have done the same for quite a while and have had lessons in various locations over that time depending on my schedule and my teachers schedule. We used to have lessons in a coffee shop which was fine a lot of the time but occasionally was a bit noisy (fortunately there are many coffee shops so moving to another was always an option). As long as you are buying something then it's not cheeky at all, you see students doing working there and people working on their laptops in there for hours on end so nothing wrong with having a language lesson.
What we do now depends on whether it is term time or not (she also teaches as a couple of language schools). During term time we actually have a lesson in a pub (no alcohol involved of course). Sit in a quiet corner out the way with a couple of soft drinks and have the lesson ... not had a problem with doing that and it's close to the language school she teaches at that evening so she can go there after my lesson. Outside term time she doesn't need to be at the language school so we actually have a lesson in a supermarket cafe which is usually quiet when we are doing it and is in a convenient location for both of us to get too.
